Mitigating negative effects of EBHSV-infected eastern cottontail invasion in Italy using Z-type control on a four-population system

The introduction in Italy of eastern cottontails (Sylvilagus floridanus) for hunting purposes has influenced the local predator-prey dynamics of the red foxes (Vulpes vulpes) and native European hares (Lepus europaeus). Although no direct competition seems to occur between the two lagomorphs, the cottontail invasion damages the indigenous hare population. Indeed, the invasive lagomorphs cause hyperpredation of red foxes on native hares and are also carriers of viruses and parasites. This paper focuses on the situation in which EBHSV-infected eastern cottontails are introduced in a region of virus-free European hares. To avoid the extinction of native lagomorphs and to contain the invasive ones, we look at two possible biological control actions using the Z-type control method on a four-population reference system. In particular, we consider an indirect control of the invasive prey acting on predators and a combination of this indirect control with direct control on native prey. The corresponding Z-controlled models are investigated analytically and numerically. In both cases, the Z-type control significantly reduces the number of equilibria and the convergence of the cottontail population to the desired state is ensured. The hare survival, instead, is guaranteed only in the second case. Overall, mathematically speaking, the second Z-type control action seems the best solution. However, in the cases in which the indirect control on cottontails allows the native prey survival, this control may be preferable since it involves only one control function and seems more practicable. In any case, in the choice of control action, ecosystem managers need to consider each specific situation, taking into account various elements from a biological and practical point of view.